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Laser Physics

Collective oscillations of vortices in Bose-Einstein condensates under rotation

K. Machida, Takeshi Mizushima, Masanori Ichioka

Published Apr 1, 2005• 0 citations
OpenAlex

Abstract

We investigate low-energy collective excitations in Bose-Einstein condensates (BECs) with a single-vortex line or many vortices by using the microscopic theory based on the Bogoliubov-Popov formalism. The paper is divided into the following two section: (i) We first study the damping process of the quadrupole modes in a three-dimensional cigar-shaped BEC. The selective excitation of such the modes occurs during the rotation of the condensate in the opposite or same direction relative to a vortex velocity field. The dramatic change of the damping process of these modes is explained by the linear response theory. It is proposed that Kelvin modes play a leading part in the decay process of the quadrupole excitation. These results are quantitatively compared with the recent experiment on 87 Rb by Bretin et al. [Phys. Rev. Lett. 90, 100403 (2003)]. (ii) In addition, the complete spectrum of the collective excitations in vortex-lattice states is obtained by solving the Bogoliubov-de Gennes equation in a two-dimensional disk-shaped BEC. We also discuss the frequency shift of totally symmetric and twofold symmetric Tkachenko modes.

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Laser Physics•Jan 1, 2004•0 citations
We investigate low-energy collective excitations in Bose-Einstein condensates (BECs) with a single-vortex line or many vortices by using the microscopic theory based on the Bogoliubov-Popov formalism. The paper is divided into the following two section: (i) We first study the damping process of the quadrupole modes in a three-dimensional cigar-shaped BEC. The selective excitation of such the modes occurs during the rotation of the condensate in the opposite or same direction relative to a vortex velocity field. The dramatic change of the damping process of these modes is explained by the linear response theory. It is proposed that Kelvin modes play a leading part in the decay process of the quadrupole excitation. These results are quantitatively compared with the recent experiment on 87 Rb by Bretin et al. [Phys. Rev. Lett. 90, 100403 (2003)]. (ii) In addition, the complete spectrum of the collective excitations in vortex-lattice states is obtained by solving the Bogoliubov-de Gennes equation in a two-dimensional disk-shaped BEC. We also discuss the frequency shift of totally symmetric and twofold symmetric Tkachenko modes.
We investigate the damping mechanism of two transverse quadrupole oscillations in the single-vortex state of Bose-Einstein condensates using the linear response theory. It is demonstrated theoretically that the Kelvin modes as a propagation wave along a vortex line can be excited via Beliaev damping processes for only the counter-rotating quadrupole mode. We calculate the spectral weight of the density-response function within the Bogoliubov-Popov theory in a cylindrical system taking into account both Beliaev and Landau processes. Furthermore, we extend these considerations to the full 3D cigar-shaped system, which enables us to discuss the effects of the longitudinal confinement on the damping processes. These results are compared with the recent experiment on 87 Rb by Bretin et al. [Phys. Rev. Lett. 90, 100403 (2003)].
The complete low-energy collective-excitation spectrum of vortex lattices is discussed for rotating Bose-Einstein condensates by solving the Bogoliubov-de Gennes equation, yielding, e.g., the Tkachenko mode recently observed at JILA. The totally symmetric subset of these modes includes the transverse shear, common longitudinal, and differential longitudinal modes. We also solve the time-dependent Gross-Pitaevskii equation to simulate the actual JILA experiment, obtaining the Tkachenko mode and identifying a pair of breathing modes. Combining both approaches allows one to unambiguously identify every observed mode.
We have calculated collective-mode spectra for three-dimensional, rotating Bose-Einstein condensates in oblate harmonic traps using the microscopic Bogoliubov--de Gennes field theory. For condensates with Nv{N}_{v}Nv​ vortices, Nv{N}_{v}Nv​ Kelvin-Tkachenko-mode branches are obtained. The features of these modes are compared with those predicted by a classical point-vortex model. We have created movies to visualize the motion of the vortices corresponding to the Kelvin-Tkachenko waves.
It is demonstrated theoretically that the counter-rotating quadrupole mode in a vortex of Bose-Einstein condensates can decay into a pair of Kelvin modes via the Beliaev process. We calculate the spectral weight of a density-response function within the Bogoliubov framework, taking account of both Beliaev and Landau processes. Good agreement with experiment on 87 Rb by Bretin et al. [Phys. Rev. Lett., 100403 (2003)]] allows us to unambiguously identify the decayed mode as the Kelvin wave propagating along a vortex line.
The splitting process of quadruply charged vortices into less charged vortices is studied at zero temperature. We solve the Bogoliubov-de Gennes (BdG) equation numerically and classify the excitations by angular momentum l relative to the condensates. Unstable modes having complex eigenvalues appear when l = 2-6. It is found that two excitations are coupled with each other when their total energy and angular momentum are zero and yield a pair of complex eigenvalues. The decay process is also numerically simulated by solving the time-dependent Gross-Pitaevskii equation. The behavior of a condensate shows good agreement with the results of BdG. The quadruply charged vortex splits into four singly quantized vortices, which are arranged as a line, triangle, and square according to the angular momentum of the excited eigenmode. We also observe the effect of nonlinearity.